Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis.pdf

Objectives

ZT

S/IS

TO

CK

PH

OT

O.C

OM

381

9

Break-Even Point and Cost-Volume-Profi t Analysis

After completing this chapter, you should be able to answer the following questions:

LO.1 What is the break-even point (BEP) and why is it important?LO.2 How is the BEP determined and what methods are used to identify BEP?LO.3 What is cost-volume-profi t (CVP) analysis and how do companies use CVP

information in decision making?LO.4 How do break-even and CVP analysis diff er for single-product and

multiproduct fi rms?LO.5 How are margin of safety and operating leverage concepts used in

business?LO.6 What are the underlying assumptions of CVP analysis?

382 Chapter 9 Break-Even Point and Cost-Volume-Profi t Analysis

LO.1 What is the break-even point (BEP) and why is it important?

IntroductionCorporate managers have a goal of maximizing shareholder wealth. However, given that no obvious, single course of action leads to fulfi llment of that goal, managers must choose a specifi c course of action and develop plans and controls to pursue that course. Because planning is future oriented, uncertainty exists and information helps reduce that uncer-tainty. Controlling is making actual performance align with plans, and information is nec-essary in that process. Much of the information managers use to plan and control refl ects relationships among product cost, selling prices, and sales volumes. Changing one of these essential components in the mix will cause changes in other components. For example, a company manager would want to estimate whether an increase in advertising expenditures for a particular product would be justifi ed by the increase in product sales volume and con-tribution margin that would be generated.

Th is chapter focuses on understanding how cost, volume, and profi t interact. Understanding these relationships helps in predicting future conditions (planning) as well as in explaining, evaluating, and acting on results (controlling). Before generating profi t, a company must fi rst reach its break-even point, which means that it must generate suffi cient sales revenue to cover all cost. Th en, by linking cost behavior and sales volume, managers can use the cost-volume-profi t model to plan and control.

Th e chapter also presents the concepts of margin of safety and degree of operating leverage. Information provided by these models helps managers focus on the implications that volume changes would have on organizational profi tability.

Break-Even PointAs discussed in Chapter 3, absorption costing is the traditional approach to product costing and is primarily used for external reporting. Alternatively, variable costing is more com-monly used for internal purposes because it makes cost behavior more transparent than does absorption costing. Th e variable costing presentation separates variable from fi xed cost and facilitates the use of this chapter’s models:

break-even point,•

cost-volume-profi t,•

margin of safety, and•

degree of operating leverage.•

A variable costing budgeted income statement for Sesame Company is presented in Exhibit 9–1. Sesame Company manufactures a high-quality line of desk clocks. Product specifi cations have been established for several years and will continue at least until model year 2012. In addition to the traditional income statement information, per-unit amounts are shown for sales revenue, variable cost, and contribution margin. Th e company has a total variable production cost of 62.5 percent, a variable selling expense of 10 percent, and a contribution margin ratio of 27.5 percent. Th ese Sesame Company data are used throughout this chapter to illustrate break-even and cost-volume-profi t computations.

A company’s break-even point (BEP) is that level of activity, in units or dollars, at which total revenue equal total cost. Th us, at BEP, the company generates neither a profi t nor a loss on operating activities. Companies, however, do not wish merely to “break even” on opera-tions. Th e BEP is calculated to establish a point of reference. Knowing BEP, managers are better able to set sales goals that should result in profi ts from operations rather than losses.

Finding the BEP fi rst requires understanding company revenues and cost. A short summary of revenue and cost assumptions is presented at this point to provide a foun-dation for BEP calculation and cost-volume-profi t (CVP) analysis. Th ese assumptions, and some challenges to them, are discussed in more detail at the end of the chapter.

Chapter 9 Break-Even Point and Cost-Volume-Profi t Analysis 383

Relevant range:• Th e company is assumed to be operating within the relevant range of activity specifi ed in determining the revenue and cost information used in each of the following assumptions.1

Revenue:• Revenue per unit is assumed to remain constant; fl uctuations in per-unit revenue for factors such as quantity discounts are ignored. Th us, total revenue fl uctuates in direct proportion to level of activity or volume.

Variable cost:• On a per-unit basis, variable costs are assumed to remain constant. Th erefore, total variable cost fl uctuates in direct proportion to level of activity or volume. Variable production costs include direct material, direct labor, and variable overhead; variable selling costs include charges for items such as commissions and shipping. Variable administrative costs can exist in areas such as purchasing; however, in the illustrations that follow, administrative costs are assumed to be fi xed.

Fixed cost:• Total fi xed costs are assumed to remain constant, and, as such, per-unit fi xed cost decreases as volume increases. (Per-unit fi xed cost increases as volume decreases.) Fixed costs include both fi xed manufacturing overhead and fi xed selling and administra-tive expenses.

Mixed cost:• Mixed costs are separated into their variable and fi xed elements before they are used in BEP or CVP analysis. Any method (such as regression analysis or the high–low method) that validly separates these costs in relation to one or more predictors can be used.

An important measure in break-even analysis is contribution margin (CM), which can be defi ned on either a per-unit or a total basis. CM per unit equals selling price per unit minus total variable cost per unit, which includes production, selling, and administrative cost. Unit contribution margin is constant because revenue and variable cost have been defi ned as being constant per unit. Total CM is the diff erence between total revenue and total variable cost for all units sold. Th is amount fl uctuates in direct proportion to sales vol-ume. On either a per-unit or a total basis, CM indicates the amount of revenue remaining after all variable costs have been covered.2 Th is amount contributes to the coverage of fi xed cost and the generation of profi t.

1 As discussed in Chapter 2, the relevant range is the range of activity over which a variable cost will remain constant per unit and a fixed cost will remain constant in total.2 Contribution margin refers to the total contribution margin. Product contribution margin is the difference between revenues and total variable product cost included in cost of goods sold.

Exhibit 9–1 Sesame Company Budgeted Income Statement for 2010

Total Per Unit Percentage

Sales (600,000 units) $24,000,000 $40.00 100.0

Variable cost

Production $15,000,000 $25.00 62.5

Selling 2,400,000 4.00 10.0

Total variable cost (17,400,000) (29.00) (72.5)

Contribution margin $ 6,600,000 $11.00 27.5

Fixed cost

Production $ 3,200,000

Selling and administrative 1,200,000

Total fi xed cost (4,400,000)

Income before income tax $ 2,200,000


LO.2 How is the BEP determined and what methods are used to identify BEP?

Identifying the Break-Even PointBreak-even calculations can be demonstrated using the formula, graph, and income statement approaches. Data needed to compute the break-even point and perform CVP analysis are given in the income statement shown in Exhibit 9–1 for Sesame Company.

Formula Approach to Breakeven

Th e formula approach to break-even analysis uses an algebraic equation to calculate the BEP. In this analysis, sales volume, rather than production activity, is the focus of the relevant range. Th e equation represents the variable costing income statement and shows the relationships among revenue, fi xed cost, variable cost, volume, and profi t as follows:

R(X) � VC(X) � FC � P

where R � revenue (selling price) per unit

X � volume (number of units)

R(X) � total revenue

VC � variable cost per unit

VC(X) � total variable cost

FC � total fi xed cost

P � total profi t

Because this equation is simply a formulaic representation of an income statement, P can be set equal to zero to solve for the break-even point. At the point where P � $0, total rev-enues are equal to total cost, and break-even point (BEP) in units can be found by solving the equation for X.

R(X) � VC(X) � FC � $0

R(X) � VC(X) � FC

(R � VC)(X) � FC

X � FC � (R � VC)

X � FC � CM

Break-even volume equals total fi xed cost divided by contribution margin per unit (rev-enue per unit minus the variable cost per unit). Using the information in Exhibit 9–1 for Sesame Company ($40 selling price per clock, $29 variable cost per clock, and $4,400,000 of total fi xed cost), the BEP for the company is calculated as

$40(X) � $29(X) � $4,400,000 � $0

$40(X) � $29(X) � $4,400,000

$11(X) � $4,400,000

X � $4,400,000 � $11

X � 400,000 clocks

BEP can be expressed in either units or dollars of revenue. One way to convert a unit BEP to dollars is to multiply the number of units by the selling price per unit. For Sesame, the BEP in sales dollars is $16,000,000 (400,000 clocks � $40 per clock).

Another method of computing BEP in sales dollars requires the computation of a contribution margin ratio (CM%), which is calculated as contribution margin divided by revenue. Th is ratio indicates what proportion of revenue remains after variable cost has been deducted from sales or that portion of the revenue dollar that can be used to cover fi xed cost and provide profi t. Th e CM% can be calculated using either per-unit, or total, revenue and variable cost information. Dividing total fi xed cost by the CM% gives the BEP in sales dollars.


For Sesame Company, the break-even sales dollars are

X � FC � [(R � VC) � R]

X � $4,400,000 � [($40 � $29) � $40]

X � $4,400,000 � ($11 � $40)

X � $4,400,000 � 0.275

X � $16,000,000

BEP in units can be determined by dividing the BEP in sales dollars by the unit selling price, or

X = $16,000,000 � $40

X = 400,000 clocks

Th e CM% allows the BEP to be determined even if unit selling price and unit variable cost are not known. Subtracting the contribution margin ratio from 100 percent gives the vari-able cost ratio (VC%), which represents variable cost as a proportion of revenue.3

Graphing Approach to Breakeven

Although solutions to BEP problems can be determined using equations, sometimes the information is more eff ectively conveyed to managers in a visual format. Exhibit 9–2 (p. 386) graphically presents each income statement item for Sesame Company’s original budgeted data (see Exhibit 9–1), providing visual representations of revenue, cost, and contribution margin behaviors.

Th e graphs presented in Exhibit 9–2 illustrate individual behaviors, but are not very useful for determining the relationships among the income statement amounts. A break-even chart can be prepared to graph the relationships among revenue, volume, and cost. Th e BEP on a break-even chart is located at the point where the total cost and total revenue lines intersect. Two approaches to graphing can be used in preparing break-even charts: the traditional approach and the profi t-volume graph approach.

Traditional ApproachTh e traditional approach break-even graph shows the relationships among revenue, cost, and profi t/loss. Th is graph does not show contribution margin. A traditional break-even graph for Sesame Company is prepared by completing the following steps.

Step 1: As shown in Exhibit 9–3 (p. 386), label each axis and graph the total cost and fi xed cost lines. Th e fi xed cost line is drawn parallel to the x-axis (volume). Th e variable cost line begins where the fi xed cost line intersects the y-axis. Th e slope of the variable cost line is the per-unit variable cost ($29). Th e resulting line represents total cost. Th e distance between the fi xed cost and the total cost lines represents total variable cost at each activity level.

Step 2: Chart the revenue line, beginning at $0. Th e BEP is located at the intersection of the revenue line and the total cost line. Th e vertical distance to the right of the BEP and between the revenue and total cost lines represents profi t; the distance between the revenue and total cost lines to the left of the BEP represents loss. If exact read-ings could be taken on the graph in Exhibit 9–4 (p. 387), the break-even point for Sesame Company would be $16,000,000 of sales, or 400,000 clocks.

3 Derivation of the contribution margin ratio formula is as follows:

Sales � [(VC%)(Sales)] � FC (1 � VC%)Sales � FC Sales � FC � (1 � VC%) because (1 � VC%) � CM% then Sales � FC � CM%

where VC% � variable cost ratio or variable cost as a percentage of sales, CM% � contribution margin ratio or contribution margin as a percentage of sales

Thus, the VC% plus the CM% is equal to 100 percent.


Exhibit 9–2 Sesame Company Graphing Presentation of Income Statement Items

300,000 400,000 500,000

Relevant Range

TR

Number of Clocks

20,000,000

16,000,000

12,000,000

Reve

nue

(in $

)

300,000 400,000 500,000

Relevant Range

TR

Number of Clocks

TR � Total Revenue TCM � Total Contribution Margin TVC � Total Variable Cost TFC � Total Fixed Cost

5,500,000

4,400,000

3,300,000

Cont

ribut

ion

Mar

gin

(in $

)

300,000 400,000 500,000Number of Clocks

14,500,000

11,600,0008,700,000

Varia

ble

Cost

(in

$)

TVC

300,000 400,000 500,000Number of Clocks

4,400,000

Fixe

d Co

st (i

n $)

Relevant Range

TVC

Relevant Range

TFC

TCM

Exhibit 9–3 Sesame Company Graph of Total and Variable Cost

$18,900,000

$4,400,000

0300,000

Number of Clocks500,000

Total Cost

Total Fixed Cost

Cost

Note: Linear functions are always assumed for total revenue, total variable cost, and total fixed cost. These functions are reflected in the basic assumptions given on pp. 401–402.


Profi t-Volume Graph

Th e profi t-volume (PV) graph provides a depiction of the amount of profi t or loss associ-ated with each sales level. Th e horizontal, or x, axis on the PV graph represents sales vol-ume; the vertical, or y, axis represents dollars of profi t or loss. Amounts shown above the x-axis are positive and represent profi ts; amounts shown below the x-axis are negative and represent losses.

Two points can be located on the graph: total fi xed cost and break-even point. Total fi xed cost is shown on the y-axis below the sales volume line as a negative amount. If no products were sold, the fi xed cost would still be incurred and a loss of that amount would result. Location of the BEP in units may be determined algebraically and is shown at the point where the profi t line intersects the x-axis; at that point, there is no profi t or loss. Th e amount of profi t or loss for any sales volume can be read from the y-axis. Th e slope of the profi t (diagonal) line is determined by the unit contribution margin ($11), and the points on the line represent the contribution margin earned at each volume level. Th e line shows that no profi t is earned until total contribution margin covers total fi xed cost.

Th e PV graph for Sesame Company is shown in Exhibit 9–5 (p. 388). Total fi xed cost is $4,400,000, and the break-even point is 400,000 clocks. Th e diagonal line refl ects the original Exhibit 9–1 income statement data indicating a profi t of $2,200,000 at a sales volume of 600,000 clocks.

Clocks sold at BEP 400,000

Sales $ 16,000,000

Total variable cost (11,600,000)

Contribution margin $ 4,400,000

Total fi xed cost (4,400,000)

Profi t before tax $ 0

Exhibit 9–4 Sesame Company Traditional Approach of Graphing Breakeven

$20,000,000

$4,400,000

$16,000,000

0400,000

Number of Clocks500,000

ContributionMargin Area

Total Revenue

Total Cost Total Variable Cost


LO.3 What is cost-volume-profi t (CVP) analysis and how do companies use CVP information in decision making?

Exhibit 9–5 Sesame Company Profi t-Volume Graph

$4,400,000

$3,300,000

$2,200,000

$1,100,000

�$1,100,000

�$2,200,000

�$3,300,000

�$4,400,000

0Pr

ofit/

Loss

700300 400 500 600Number of Clocks (in thousands)

800 900

BEP

PROFIT

LOSS

Total Fixed Cost

Th e graphing approach to breakeven provides a detailed visual display of the BEP. It does not, however, provide a precise solution because exact points cannot be determined on a graph. A defi nitive computation of the BEP can be found algebraically using the formula approach or a computer software application. A third approach to illustrating breakeven is the income statement approach.

Income Statement Approach

Th e income statement approach to fi nding BEP allows accountants to prepare budgeted statements using available revenue and cost information. Income statements can also be used to prove the accuracy of computations made using the BEP formulas or graphs. Because the formula, graphing, and income statement approaches are based on the same relationships, each should align with the other. Following is the income statement proving the prior cal-culations of the BEP for Sesame Company. Because the profi t before tax is $0, the income statement supports the break-even point determinations of the other methods.

Th e BEP provides a starting point for planning future operations. Managers want to earn operating profi t rather than simply cover costs. Substituting an amount other than zero for the profi t (P) term in the break-even formula converts break-even analysis to cost-volume-profi t analysis.

CVP AnalysisBecause profi t cannot be achieved until the BEP is reached, the starting point of CVP analysis is the break-even point. Examining shifts in cost and volume and the resulting eff ects on profi ts is called cost-volume-profi t (CVP) analysis. CVP analysis can be used to calculate the sales volume necessary to achieve a target profi t, stated as either a fi xed or variable amount on a before- or after-tax basis.

Managers use CVP analysis to eff ectively plan and control by concentrating on the rela-tionships among revenues, cost, volume changes, taxes, and profi t. Th e CVP model can be expressed mathematically or graphically. Th e CVP model considers all costs, regardless of whether they are product, period, variable, or fi xed. Th e analysis is usually performed on a


companywide basis. Th e same basic CVP model and calcu-lations can be applied to a single- or multiproduct business.

CVP analysis requires substitution of known amounts in the formula to solve for an unknown amount. Th e for-mula mirrors the income statement when known amounts are used for selling price per unit, variable cost per unit, volume of units, and fi xed cost to fi nd the amount of profi t generated under given conditions. Because CVP analysis is concerned with relationships among the elements aff ect-ing continuing operations, in contrast with nonrecurring activities and events, profi ts—as used in this chapter—refer to operating profi ts before extraordinary and other nonoperating, nonrecurring items. Th e following quote indicates the pervasive utility of the CVP model:

Cost Volume Profi t analysis (CVP) is one of the most

hallowed, and yet one of the simplest, analytical tools

in management accounting. [CVP] allows managers

to examine the possible impacts of a wide range of

strategic decisions [in] such crucial areas as pricing

policies, product mixes, market expansions or con-

tractions, outsourcing contracts, idle plant usage, dis-

cretionary expense planning, and a variety of other

important considerations in the planning process.

Given the broad range of contexts in which CVP can

be used, the basic simplicity of CVP is quite remark-

able. Armed with just three inputs of data—sales

price, variable cost per unit, and fi xed cost—a mana-

gerial analyst can evaluate the eff ects of decisions that

potentially alter the basic nature of a fi rm.4

An important application of CVP analysis allows managers to set a desired target profi t and focus on the relationships between it and other known income statement amounts to fi nd an unknown. One common unknown in such applications is the sales volume that is needed to generate a particular profi t amount.

Selling price is generally not as commonly unknown as volume because selling price is often market determined and is not a management decision variable. Additionally, because selling price and volume are often directly related and because certain costs are considered fi xed, managers can use CVP to determine how high variable cost can be while allowing the company to produce a desired amount of profi t. Variable cost can be aff ected by modifying product specifi cations or material quality as well as by being more effi cient or eff ective in the production, service, and/or distribution processes.

Th e following examples continue using the Sesame Company data with diff erent amounts of target profi t.

Fixed Amount of Profi t

Because contribution margin represents the sales dollars remaining after variable cost is cov-ered, each dollar of CM generated by product sales goes fi rst to cover fi xed cost and then to produce profi ts. After the BEP is reached, each dollar of CM is a dollar of before-tax profi t.

Before TaxProfi t can be treated in the break-even formula as an additional cost to be covered. Inclusion of a target profi t changes the break-even formula to a CVP equation.

4 Flora Guidry, James O. Horrigan, and Cathy Craycraft, “CVP Analysis: A New Look,” Journal of Managerial Issues (Spring 1998), pp. 74ff.

CO

RB

IS/J

UP

ITE

R IM

AG

ES

A product's selling price is often market-related rather than being a management decision variable.


R(X) � VC(X) � FC � PBT


X � (FC � PBT) � (R � VC)

or

X� (FC � PBT) � CM

where PBT � fi xed amount of profi t before tax.

Assume that Sesame’s management desires a $3,300,000 before-tax profi t. Th e calculations in Exhibit 9–6 show that to achieve this profi t before tax, the company must sell 700,000 clocks and generate $28,000,000 of revenue.

After TaxIn choosing a target profi t amount, managers must recognize that income tax represents a signifi cant infl uence on business decision making. A company wanting a particular amount of profi t after tax must fi rst determine, given the applicable tax rate, the amount of profi t that must be earned on a before-tax basis. Th e CVP formulas that designate a fi xed after-tax profi t amount are as follows:

PBT � [(TR)(PBT)] � PAT

and

R(X) � VC(X) � FC � [(TR)(PBT)] � PAT

where PBT � fi xed amount of profi t before tax PAT � fi xed amount of profi t after tax TR � tax rate

PAT is further defined so that it can be integrated into the original CVP formula:

PBT (1 � TR) � PAT

or

PBT � PAT � (1 � TR)

In units:

Profi t before tax (PBT) desired � $3,300,000


CM(X) � FC � PBT

($40 � $29)X � $4,400,000 � $3,300,000

$11X � $7,700,000

X � $7,700,000 � $11 � 700,000 clocks

In sales dollars:

Sales � (FC � PBT) � CM%

Sales � $7,700,000 � 0.275*

Sales � $28,000,000

Exhibit 9–6 Sesame Company CVP Analysis—Fixed Amount of Profi t before Tax

*From Exhibit 9–1.


Specifi c Amount of Profi t per Unit

Managers may want to conduct an analysis of profi t on a per-unit basis. As in the prior examples, profi t can be stated on either a before-tax or an after-tax basis. For these alternatives, the CVP formula must be adjusted to recognize that profi t is related to volume of activity.

Before TaxIn this situation, the adjusted CVP formula for computing the necessary unit sales volume to earn a specifi ed amount of profi t before tax per unit is

R(X) � VC(X) � FC � PuBT(X)

where PuBT � amount of profi t per unit before tax

Solving for X (volume) gives the following:

R(X) � VC(X) � PuBT(X) � FC

CM(X) � PuBT(X) � FC

X � FC � (CM � PuBT)

Th e per-unit profi t is treated in the CVP formula as if it were an additional variable cost to be covered. Th is treatment eff ectively “adjusts” the original contribution margin and

Substituting into the formula,



(R � VC)(X) � FC � [PAT � (1 � TR)]

CM(X) � FC � [PAT � (1 � TR)]

Assume Sesame Company managers set an earnings target of $3,300,000 after tax and the company’s average tax rate is 25 percent. Th e number of clocks (800,000) and dollars of sales ($32,000,000) needed to achieve that target are calculated in Exhibit 9–7.

In units:

PAT desired � $3,300,000; tax rate � 25%

PBT � PAT � (1 � TR)

PBT � $3,300,000 � (1 � 0.25)

PBT � $3,300,000 � 0.75

PBT � $4,400,000

CM(X) � FC � PBT

$11X � $4,400,000 � $4,400,000

$11X � $8,800,000

X � $8,800,000 � $11

X � 800,000 clocks

In sales dollars:

Sales � (FC � PBT) � CM ratio

Sales � ($4,400,000 � $4,400,000) � 0.275

Sales � $8,800,000 � 0.275

Sales � $32,000,000

Exhibit 9–7 Sesame Company CVP Analysis—Fixed Amount of Profi t after Tax


contribution margin ratio. When setting the desired profi t as a percentage of selling price, the profi t percentage cannot exceed the contribution margin ratio. If it does, an infeasible problem is created because the “adjusted” contribution margin is negative. In such a case, the variable cost ratio plus the desired profi t percentage would exceed 100 percent of the selling price, and such a condition cannot exist.

Assume that Sesame’s president wants to know what level of sales (in clocks and dollars) would be required to earn a 15 percent before-tax profi t on sales. Th is rate of return translates into a set amount of profi t per unit of $6. Th e calculations shown in Exhibit 9–8 provide the answers to these questions.

After TaxAdjusting the CVP formula to determine unit profi t on an after-tax basis involves stating profi t in relation to both the volume and the tax rate. Algebraically, the formula is:

R(X) � VC(X) � FC � {(TR)[PuBT(X)]} � PuAT(X)

where PuAT � amount of profi t per unit after tax

PuAT is further defi ned so that it can be integrated into the original CVP formula:

PuAT(X) � PuBT(X) � {(TR)[PuBT(X)]}

PuAT(X) � PuBT(X)[(1 � TR)]

PuBT(X) � [PuAT � (1 � TR)](X)

Exhibit 9–8 Sesame Company CVP Analysis—Set Amount of Profi t per Unit before Tax

In units:

PuBT desired � 15% of sales revenue

PuBT � 0.15($40)

PuBT � $6


$11X � $6X � $4,400,000

$5X � $4,400,000

X � 880,000 clocks

In sales dollars, the following relationships exist:

Per Clock Percentage

Selling price $ 40 100.0

Variable cost (29) (72.5)

Set amount of profi t before tax (6) (15.0)

“Adjusted” contribution margin ratio $ 5 12.5

Sales � FC � “Adjusted” CM%*

Sales � $4,400,000 � .125

Sales � $35,200,000

*It is not necessary to have per-unit data; all computations can be made with percentage information only.


Exhibit 9–10 (p. 394) proves each of the computations made in Exhibits 9–6 through 9–9 for Sesame Company. Th e answers provided by break-even or CVP analysis are valid only in relation to specifi c selling price and cost relationships. Changes that occur in the company’s selling price or cost structure will cause a change in the BEP or in the sales needed to obtain a desired profi t. However, the eff ects of revenue and cost changes on a company’s BEP or sales volume can be determined through incremental analysis.

Incremental Analysis for Short-Run Changes

Th e break-even point can increase or decrease, depending on revenue and cost changes. Other things being equal, the BEP will increase if there is an increase in the total fi xed cost or a decrease in the unit (or percentage) contribution margin. A decrease in contribution margin could arise because of a reduction in selling price, an increase in variable cost per

Th us, the following relationship exists:

R(X) � VC(X) � FC � [PuAT � (1 � TR)](X)

CM(X) � FC � PuBT(X)


X � FC � (CM � PuBT)

Sesame’s managers want to earn an after-tax profi t of 10 percent of revenue and the company has a 25 percent tax rate. Th e necessary sales in units and dollars are given in Exhibit 9–9.

Exhibit 9–9 Sesame Company CVP Analysis—Set Amount of Profi t per Unit after Tax

In units:

PuAT desired � 10% of revenue; tax rate � 25%

PuAT � 0.10($40)

PuAT � $4

PuBT � $4 � (1.00 � 0.25)

PuBT � $4 � 0.75

PuBT � $5.33 (rounded)


$11.00X � $5.33X � $4,400,000

$5.67X � $4,400,000

X � $4,400,000 � $5.67

X � 776,014 clocks (rounded)

Per Clock Percentage

Selling price $40.00 100.00

Variable cost (29.00) (72.50)

Set amount of profi t before tax (5.33) (13.33) (rounded)

“Adjusted” contribution margin $ 5.67 14.17

Sales � FC � “Adjusted” CM ratio

Sales � $4,400,000 � 0.1417

Sales � $31,051,517 (rounded)


unit, or a combination of the two. Th e BEP will decrease if total fi xed cost decreases or unit (or percentage) contribution margin increases. A change in the BEP will also cause a shift in total profi t or loss at any level of activity.

Incremental analysis is a process that focuses only on factors that change from one course of action or decision to another. In CVP situations, incremental analysis is focused on changes occurring in revenue, cost, and/or volume. Following are some examples of changes that could occur in a company and the incremental computations that can be used to determine the eff ects of those changes on the BEP or on profi t. In most situations, incremental analysis is suffi cient to determine the feasibility of contemplated changes, and a complete income statement need not be prepared. Th e basic facts presented for Sesame Company in Exhibit 9–1 are continued. All of the following examples use before-tax infor-mation to simplify the computations. After-tax analysis would require the application of the (1 � tax rate) adjustment to all profi t fi gures.

Case 1Sesame Company wants to earn a before-tax profi t of $2,750,000. How many clocks must the company sell to achieve that profi t? Th e incremental analysis relative to this question addresses the number of clocks above the BEP that must be sold. Because each dollar of contribution margin after BEP is a dollar of profi t, the incremental analysis focuses only on the profi t desired:

$2,750,000 � $11 � 250,000 clocks above BEP

Exhibit 9–10 Sesame Company’s Income Statement Approach to CVP—Proof of Computations

Previous computations:

Break-even point: 400,000 clocks

Fixed profi t ($255,000) before tax: 700,000 clocks

Fixed profi t ($3,300,000) after tax: 800,000 clocks

Set amount of profi t (15% on revenues) before tax: 880,000 clocks

Set amount of profi t (10% on revenues) after tax: 776,014 clocks

R � $40 per clock; VC � $29 per clock; FC � $4,400,000

Tax rate � 25% for Exhibits 9–3 and 9–5

Clocks SoldBasic Data

400,000Exh. 9–6 700,000

Exh. 9–7 800,000

Exh. 9–8 880,000

Exh. 9–9 776,014

Sales $16,000,000 $28,000,000 $32,000,000 $35,200,000 $31,040,560

Total variable cost (11,600,000) (20,300,000) (23,200,000) (25,520,000) (22,504,406)

Contribution margin $ 4,400,000 $ 7,700,000 $ 8,800,000 $ 9,680,000 $ 8,536,154

Total fi xed cost (4,400,000) (4,400,000) (4,400,000) (4,400,000) (4,400,000)

Profi t before tax $ 0 $ 3,300,000 $ 4,400,000 $ 5,280,000a $ 4,136,154

Tax (25%) (1,100,000) (1,034,039)

Profi t after tax (NI) $ 3,300,000 $ 3,102,115b

a Desired profit before tax � 15% on revenue; 0.15 × $35,200,000 � $5,280,000. b Desired profit after tax � 10% on revenue; 0.10 × $31,040,560 � $3,104,056 (differs from $3,102,115 only because of

rounding error).


Because the BEP has already been computed as 400,000 clocks, the company must sell a total of 650,000 clocks.

Case 2Sesame Company estimates that spending an additional $425,000 on advertising will result in an additional 50,000 clocks being sold. Should the company incur this extra fi xed cost? Th e contribution margin from the additional clocks must fi rst cover the additional fi xed cost before additional profi ts can be generated.

Increase in contribution margin (50,000 clocks × $11 CM per clock) $550,000

� Increase in fi xed cost (425,000)

� Net incremental benefi t $125,000

Because there is a net incremental profi t of $125,000, the company should undertake the advertising campaign.

An alternative computation is to divide the additional fi xed cost of $425,000 by the $11 contribution margin. Th e result indicates that 38,636 clocks (rounded) would be required to cover the additional cost. Because the company expects to sell 50,000 clocks, the remaining 11,364 clocks would produce $11 of profi t per clock, or $125,004.

Case 3Sesame Company estimates that reducing a clock’s selling price to $37.50 will result in an additional 90,000 clocks per year being sold. Should the company reduce the clock’s selling price? Budgeted sales volume, given in Exhibit 9–1, is 600,000 clocks. If the selling price is reduced, the contribution margin per unit will decrease to $8.50 per clock ($37.50 SP � $29.00 VC). Sales volume will increase to 690,000 clocks (600,000 � 90,000).

Total new contribution margin (690,000 clocks × $8.50 CM per clock) $5,865,000

� Total fi xed cost (unchanged) (4,400,000)

� New profi t before tax $1,465,000

� Current budgeted profi t before tax (from Exhibit 9–1) (2,200,000)

� Net incremental loss $ (735,000)

Because the reduction in sales price will cause profi t to decrease by $735,000, Sesame Company should not reduce the clock’s selling price. Th e company, however, might want to investigate the possibility that a reduction in price could, in the long run, increase demand to more than the additional 90,000 clocks per year and, thus, make the price reduction a profi table action.

Case 4Sesame Company has an opportunity to sell 100,000 clocks to a nonrecurring customer for $27 per clock. Th e clocks will be packaged and sold using the customer’s own logo. Packaging cost will increase by $1 per clock, but the company will not incur any of the current variable selling cost. If Sesame accepts the job, it will pay a $30,000 commission to the salesperson calling on this customer. Th is sale will not interfere with budgeted sales and is within the company’s relevant range of activity. Should Sesame make this sale?

Th e new variable cost per clock is $26 ($25 total budgeted variable production cost � $1 additional variable packaging cost � $0 variable selling cost). Th e $27 selling price minus the


LO.4 How do break-even and CVP analysis diff er for single-product and multiproduct fi rms?

$26 new total variable cost provides a contribution margin of $1 per clock sold to the nonre-curring customer.

Total additional contribution margin (100,000 clocks × $1 CM per clock) $100,000

� Additional fi xed cost (commission) related to this sale (30,000)

� Net incremental benefi t $ 70,000

Th e total CM generated by the sale more than covers the additional fi xed cost. Th us, the sale produces incremental profi t and, therefore, should be made.

However, as with all proposals, this one should be evaluated on the basis of its long-range potential. Is the commission a one-time payment? Will the customer possibly return in future years to buy additional clocks? Will such sales aff ect regular business in the future? Is the sales price to the new customer a legal one?5 If all of these questions can be answered “yes,” Sesame should seriously consider this opportunity. In addition, referral business by the new customer could also increase sales.

Th e incremental approach is often used to evaluate alternative pricing strategies in eco-nomic downturns. In such stressful times, companies must confront the reality that they might be unable to sell a normal volume of goods at normal prices. With this understanding, companies can choose to maintain normal prices and sell a lower volume of goods or reduce prices and attempt to maintain market share and normal volume.

CVP Analysis in a Multiproduct EnvironmentCompanies typically produce and sell a variety of products, some of which may be related (such as bats and baseballs or sheets, towels, and bedspreads). To perform CVP analysis in a multiproduct company, one must assume either that

the product sales mix stays constant as total sales volume changes or•

that the average contribution margin ratio stays constant as total sales volume changes.•

Th e constant mix assumption can be referred to as the “bag” (or “basket”) analogy. Th e anal-ogy is that the sales mix represents a bag of products that are sold together. For example, when some product A is sold, set amounts of products B and C are also sold. Use of an assumed constant sales mix allows a weighted average contribution margin ratio to be com-puted for the bag of products being sold. Without the assumption of a constant sales mix, BEP cannot be calculated, nor can CVP analysis be used eff ectively.6

In a multiproduct company, the CM% is weighted by the quantities of each product included in the “bag.” Th is weighting process means that the CM% of the product compos-ing the largest proportion of the bag has the greatest impact on the average contribution margin of the product mix.

Suppose that, because of the success of its desk clocks, Sesame management is consider-ing the production of clock wall-mounting kits. Th e vice president of marketing estimates that, for every three clocks sold, the company will sell one clock wall-mounting kit. Th erefore, the “bag” of products has a 3:1 product ratio. Sesame will incur an additional $514,000 in fi xed plant asset cost (depreciation, insurance, and so forth) to support a higher relevant range of production. Exhibit 9–11 provides relevant company information and shows the break-even computations. Breakeven occurs at sales of 126,000 “bags” of product, which contain 378,000 clocks and 126,000 wall-mounting kits.

5 The Robinson-Patman Act addresses the legal ways in which companies can price their goods for sale to different purchasers.6 After the constant percentage contribution margin in a multiproduct firm has been determined, all situations regarding profit points can be treated in the same manner as they were earlier in the chapter. One must remember, however, that the answers reflect the “bag” assumption.


Exhibit 9–11 Sesame Company CVP Analysis—Multiple Products

ClocksClock

Wall-Mounting Kits

Product Cost Information (Percentage) (Percentage)

Selling price $40 100.0 $10 100

Total variable cost (29) (72.5) (4) (40)

Contribution margin $11 27.5 $ 6 60

Total fi xed cost (FC) � $4,400,000 previous � $514,000 additional � $4,914,000

ClocksClock Wall-

Mounting Kits Total Percentage

Number of products per bag 3 1

Revenue per product $40 $10

Total revenue per "bag" $120 $10 $130 100

Variable cost per product (29) (4)

Total variable cost per "bag" (87) (4) (91) (70)

Contribution margin—product $11 $ 6

Contribution margin—"bag" $ 33 $ 6 $ 39 30

BEP in units (where B � number of "bags" of products)

CM(B) � FC

$39B � $4,914,000

B � 126,000 bags

Note: Each "bag" consists of 3 clocks and 1 clock wall-mounting kit; therefore, it will take 378,000 clocks and 126,000 clock wall-mounting kits to break even, assuming the con-stant 3:1 mix.

BEP in sales dollars (where S$ � sales dollars; CM% � weighted average CM per "bag")

S$ � FC � CM%

S$ � $4,914,000 � 0.30

S$ � $16,380,000

Note: The break-even sales dollars also represent the assumed constant sales mix of $120 of clocks to $10 of clock wall-mounting kits to represent a 92.3% (rounded) to 7.7% (rounded) ratio. Thus, the company must have $15,120,000 ($16,380,000 � 92.3%) in sales of clocks and $1,260,000 in sales of clock wall-mounting kits to break even.

Proof of these computations using the income statement approach:

Clocks Clock Wall-Mounting Kits Total

Sales $15,120,000 $1,260,000 $16,380,000

Variable cost (10,962,000) (504,000) (11,466,000)

Contribution margin $ 4,158,000 $ 756,000 $ 4,914,000

Fixed cost (4,914,000)

Income before tax $ 0


Any shift in the product sales mix will change the weighted average CM% and BEP. If the sales mix shifts toward a product with a lower dollar contribution margin, the BEP will increase and profi ts will decrease unless there is a corresponding increase in total revenues. A shift toward higher dollar contribution margin products without a corresponding decrease in revenues will cause a lower BEP and increase profi ts. Th e fi nancial results shown in Exhibit 9–12 indicate that a shift toward the product with the lower dollar contribution margin (clock wall-mounting kits) causes a higher BEP and lower profi ts. Th is exhibit assumes that Sesame sells 126,000 “bags” of product (the break-even level in Exhibit 9–11), but the mix was not in the exact proportions assumed in Exhibit 9–11. Instead of a 3:1 ratio, the sales mix was 2.5 clocks to 1.5 clock wall-mounting kits. A loss of $315,000 resulted because Sesame sold a higher propor-tion of the clock wall-mounting kits, which have a lower unit contribution margin than the clocks.

Exhibit 9–12 Sesame Company’s Eff ects of Product Mix Shift

ClocksClock Wall-

Mounting Kits Total Percentage

Number of products per bag 2.5 1.5

Revenue per product $40 $10

Total revenue per “bag” $100.00 $15 $115.00 100.0

Variable cost per product (29) (4)

Total variable cost per “bag” (72.50) (6) (78.50) (68.3)

Contribution margin— product $11 $ 6

Contribution margin— "bag" $ 27.50 $ 9 $ 36.50 31.7

BEP in units (where B � number of “bags” of products)

CM(B) � FC

$36.50B � $4,914,000

B � 134,631 bags (rounded up)

Actual results: 126,000 “bags” with a sales mix ratio of 2.5 clocks to 1.5 clock wall-mounting kits; thus, the company sold 315,000 clocks and 189,000 clock wall-mounting kits.

315,000 Clocks189,000 Clock

Wall-Mounting Kits Total

Sales $12,600,000 $1,890,000 $14,490,000

Variable cost (9,135,000) (756,000) (9,891,000)

Contribution margin $ 3,465,000 $1,134,000 $ 4,599,000

Fixed cost (4,914,000)

Net loss $ (315,000)


LO.5 How are margin of safety and operating leverage concepts used in business?

Managing Risk of CVP RelationshipsCVP relationships can be formally analyzed using standard metrics to evaluate risk/reward relationships at existing sales levels or prospective sales levels. Two of these metrics are margin of safety and degree of operating leverage.

Margin of Safety

When making decisions about business opportunities and changes in sales mix, managers often consider the margin of safety (MS), which is the excess of budgeted or actual sales over break-even sales. Th e MS is the amount that sales can drop before reaching the BEP and, thus, provides a measure of the amount of “cushion” against losses.

Th e MS can be expressed in units, in dollars, or as a percentage (MS%). Th e following formulas are applicable:

Margin of safety in units � Actual sales in units � Break-even sales in units

Margin of safety in $ � Actual sales in $ � Break-even sales in $

Margin of safety % � Margin of safety in units � Actual unit sales

or

MS% � Margin of safety in $ � Actual sales $

Th e BEP for Sesame based on the Exhibit 9–1 data is 400,000 units or $16,000,000 of sales. Th e company’s budgeted income statement presented in Exhibit 9–1 shows sales for 2010 of $24,000,000 for 600,000 clocks. Sesame’s MS is quite high because the company is operating far above its BEP (see Exhibit 9–13).

MS calculations allow management to determine how close to a “danger level” the company is operating and, as such, provide an indication of risk. Th e lower the MS, the more carefully management must watch revenue and control cost to avoid operating losses. At low margins of safety, managers are less likely to take advantage of opportunities that, if incorrectly analyzed or forecasted, could send the company into a loss position.

Operating Leverage

Another measure that is closely related to the MS and provides useful management information is the company’s degree of operating leverage. Th e relationship between a company’s variable and fi xed costs is refl ected in its operating leverage. Typically, highly labor-intensive organizations have high variable cost and low fi xed cost; these organizations have low operating leverage. (An exception to this rule is a sports team, which is highly labor intensive, but its labor cost is fi xed rather than variable.)

Exhibit 9–13 Sesame Company’s Margin of Safety

In units: 600,000 actual � 400,000 BEP � 200,000 clocks

In sales $: $24,000,000 actual sales � $16,000,000 BEP sales � $8,000,000

As a percentage: 200,000 � 600,000 � 33.33%

or

$8,000,000 � $24,000,000 � 33.33%


Conversely, organizations that are highly capital intensive or automated have cost structures that include low variable and high fi xed cost, providing high operating lever-age. Because variable cost is low relative to selling price, the contribution margin is high. However, high fi xed cost means that BEP also tends to be high. If the market predomi-nantly sets selling prices, volume has the primary impact on profi tability. As companies become more automated, they face this type of cost structure and become more dependent on volume increases to raise profi ts. Th us, a company’s cost structure strongly infl uences the degree to which its profi ts respond to sales volume changes.

Companies with high operating leverage have high contribution margin ratios. Although such companies must establish fairly high sales volumes to initially cover fi xed cost, once that cost is covered, each unit sold after breakeven adds signifi cantly to profi ts. Th us, a small increase in sales can have a major impact on a company’s profi ts.

Th e degree of operating leverage (DOL) measures how a percentage change in sales from the current level will aff ect company profi ts. In other words, DOL indicates how sensitive the company’s profi t is to sales volume increases and decreases. Th e computation for DOL follows.

DOL � CM � Profit before tax

Th is calculation assumes that fi xed costs do not increase when sales increase.

Assume that Sesame Company is currently selling 600,000 clocks. Th e income state-ment in Exhibit 9–14 refl ects this sales level and shows that the company has a DOL of 3.00. If Sesame increases sales by 20 percent, the 60 percent change in profi ts equals the DOL multiplied by the percentage change in sales or (3.00 � 20%). If sales decrease by the same 20 percent, the impact on profi ts is a negative 60 percent. Th ese amounts are confi rmed in Exhibit 9–14.

Th e DOL decreases as sales move upward from the BEP. Th us, when the margin of safety is low, the degree of operating leverage is high. In fact, at the BEP, the DOL is infi nite because any increase from zero is an infi nite percentage change. If a company is operating close to BEP, each percentage increase in sales can make a dramatic impact on net income. As sales increase from the break-even point, margin of safety increases but the

Exhibit 9–14 Sesame Company’s Degree of Operating Leverage

Current(600,000 clocks)

20 Percent Increase (720,000 clocks)

20 Percent Decrease (480,000 clocks)

Sales $24,000,000 $28,800,000 $19,200,000

Variable cost ($29.00 per clock) (17,400,000) (20,880,000 (13,920,000)

Contribution margin $ 6,600,000 $ 7,920,000 $ 5,280,000

Fixed cost (4,400,000) (4,400,000) (4,400,000)

Profi t before tax $ 2,200,000 $ 3,520,000a $ 880,000b

Degree of operating leverage � Contribution margin � Profi t before tax

($6,600,000 � $2,200,000) 3.00

($7,920,000 � $3,520,000) 2.25

($5,280,000 � 880,000) 6.00

aProfit increase � $3,520,000 � $2,200,000 � $1,320,000 (or 60.00% of the original profit).bProfit decrease � $880,000 � $2,200,000 � ($1,320,000) (or −60% of the original profit).


LO.6 What are the underlying assumptions of CVP analysis?

Underlying Assumptions of CVP AnalysisCVP analysis is a short-run model that focuses on relationships among selling price, variable cost, fi xed cost, volume, and profi t. Th is model is a useful planning tool that can provide information about the impact on profi t when changes are made in the cost struc-ture or in the sales level. Although limiting the accuracy of the results, several important but necessary assumptions are made in the CVP model. Th ese assumptions follow:

1. All revenue and variable cost behavior patterns are constant per unit and linear within the relevant range.

2. Total contribution margin (total revenue � total variable cost) is linear within the rel-evant range and increases proportionally with output. Th is assumption follows directly from assumption 1.

3. Total fi xed cost is constant within the relevant range. Th is assumption, in part, indicates that no capacity additions will be made during the period under consideration.

4. Mixed costs can be accurately separated into fi xed and variable elements. Although accuracy of separation can be questioned, reliable estimates can be developed from the use of regression analysis or the high–low method (as discussed in Chapter 3).

5. Sales and production are equal; thus, there is no material fl uctuation in inventory lev-els. Th is assumption is necessary because fi xed cost can be allocated to inventory at a diff erent rate each year. Th us, variable costing information must be available. Because CVP and variable costing both focus on cost behavior, they are distinctly compatible with one another.

6. In a multiproduct fi rm, the sales mix remains constant. Th is assumption is necessary so that a weighted average contribution margin and CM% can be computed.

Exhibit 9–15 Sesame Company’s Margin of Safety and Degree of Operating Leverage Relationship

Break-even sales � 400,000 units; Current sales � 600,000 units

Margin of safety % � Margin of safety in units � Actual sales in units

� [(600,000 � 400,000) � 600,000]

� 0.33, or 33% (rounded)

Degree of operating leverage � Contribution margin � Profit before tax

� $6,600,000 � $2,200,000

� 3

Margin of safety � (1 � DOL) � (1 � 3) � 0.33, or 33% (rounded)

Degree of operating leverage � (1 � MS%) � (1 � 0.33) � 3 (rounded)

degree of operating leverage declines. Th e relationship between the MS percentage (MS%) and DOL is as follows:

MS% � 1 � DOL

DOL � 1 � MS%

Th is relationship is proved in Exhibit 9–15 using the 600,000-clock sales level infor-mation for Sesame. Th erefore, if one of the two measures is known, the other can be easily calculated.


7. Labor productivity, production technology, and market conditions will not change. If any of these changes were to occur, cost would change correspondingly, and selling prices might change. Such changes would invalidate assumptions 1 through 3.

Th ese assumptions limit the activity volume for which the calculations can be made as well as the time frame for the usefulness of the calculations. If changes occur in selling price or cost, new computations must be made for break-even and CVP analyses.

Th e preceding seven assumptions are the traditional ones associated with CVP anal-ysis. An additional assumption must be noted with regard to the distinction between variable and fi xed cost. Accountants have generally assumed that cost behavior, once clas-sifi ed, remains constant as long as operations remain within the relevant range. Th us, for example, once a cost was determined to be “fi xed,” it would be fi xed next year, the year after, and 10 years from now.

It is more appropriate, however, to regard fi xed cost as long-term variable cost. Over the long run, through managerial decisions, companies can change fi xed cost; thus, a fi xed cost is not fi xed forever. Generating cost information in a manner that yields a longer-run perspective is presented in Chapter 4 on activity-based costing/management. Part of the traditional “misclassifi cation” of fi xed cost has been caused by improperly specifying driv-ers of cost. As production and sales volumes are less often viewed as cost drivers, compa-nies will begin to recognize that a “fi xed cost” exists only in a short-term perspective.

Such a reclassifi cation of cost simply means that cost drivers for long-term variable cost must be specifi ed in break-even and CVP analyses. Th e formula will need to be expanded to include these additional drivers, and more information and a longer time frame will be needed to make the calculations. No longer will sales volume necessarily be the overriding nonmonetary force in the computations.

Th ese adjustments to the CVP formula will force managers to take a long-run, rather than a short-run, view of product opportunities. Such a perspective could produce better organizational decisions. As the time frame is extended, both the time value of money and life cycle costing become necessary considerations. Additionally, the traditional income statement becomes less useful for developing projects that will take several years to mature. A long-run perspective is important in a variety of circumstances, such as when variable or fi xed costs arise only in the fi rst year that a product or service is provided to customers.

Comprehensive Review Module

Key Terms

break-even chart, p. 385

break-even point (BEP), p. 382

contribution margin ratio (CM%), p. 384

cost-volume-profi t (CVP) analysis, p. 388

degree of operating leverage (DOL), p. 400

incremental analysis, p. 394

margin of safety (MS), p. 399

operating leverage, p. 399

profi t-volume (PV) graph, p. 387

variable cost ratio (VC%), p. 385


Chapter Summary

LO.1 Determining the Break-Even Point (BEP)

BEP identifi es the volume level separating losses from profi ts.•

BEP requires organizing costs by behavior.•

BEP requires assumption of linear revenue and cost behavior.•

BEP relies on the existence of a relevant range of activity.•

LO.2 Identifying the Break-Even Point

BEP can be determined using the•

following formulas for X: -

X ➢ � Fixed Cost � Contribution Margin per Unit, where X � BEP in units

X ➢ � Fixed Cost � Contribution Margin Ratio, where X � BEP in sales dollars

graphing approach -

by reading the ➢ y-axis at the point where the total revenue and total cost lines intersect using the traditional CVP graph.

by reading where the profi t line intersects the ➢x-axis using the profi t-volume graph.

income statement approach, which -

requires developing complete income statements ➢showing total revenue minus total cost as being equal to a profi t fi gure.

is often used to prove the solutions found with ➢other approaches.

LO.3 CVP Analysis

CVP analysis can be used by a company to•

determine BEP by assigning a zero value to the profi t fi gure. -

study the interrelationships of -

prices, ➢

volumes, ➢

fi xed and variable costs, and ➢

contribution margins. ➢

calculate the level of sales volume necessary to achieve -specifi c before- or after-tax target profi t objectives.

enhance a manager’s ability to positively infl uence -current operations and to predict future operations, thereby reducing the risk of uncertainty.

LO.4 BEP and CVP Analysis for Single-Product and Multi-product Firms

In a multiproduct environment, break-even and CVP • analysis

require that a constant product sales mix or “bag” -assumption be used for the various products.

require that a weighted average contribution margin -or CM ratio be calculated for each “bag” of product sold.

state solutions in terms of “bags” of product, which -means the solutions must be converted (using the original product sales mix) to actual units (or sales dollars) of individual products.

LO.5 MS and DOL

Companies use the margin of safety (MS) and degree of • operating leverage (DOL) concepts as follows:

the MS indicates how far (in units, in sales dollars, -or as a percentage) a company is operating from its BEP; the MS% is equal to (1 � DOL).

the DOL shows the percentage change that would -occur in profi t given a specifi ed percentage change in sales from the current level; the DOL is equal to (1 � MS%).

LO.6 Underlying Assumptions of CVP Analysis

Th e break-even and CVP models are based on several • assumptions that limit their ability to refl ect reality. Underlying assumptions are that

revenue and variable cost per unit are constant and -linear within the relevant range.

contribution margin is linear within the relevant -range.

total fi xed cost is constant within the relevant range. -

mixed cost can be accurately separated into its vari- -able and fi xed components.

sales and production levels are equal. -

sales mix is constant in a multiproduct setting. -

labor productivity, production technology, and mar- -ket conditions will not change during the period under consideration.

Solution Strategies

Cost-Volume-Profi t (CVP), p. 388Th e basic equation for break-even and CVP problems is

Total Revenue � Total Cost � Profit


CVP problems can also be solved by using a numerator/denominator approach. All numer-ators and denominators and the types of problems that each relates to follow. Th e formulas relate to both single- and multiproduct fi rms, but results for multiproduct fi rms are per bag and should be converted to units of individual products.

Problem Situation Numerator Denominator

Simple BEP in units FC CM

Simple BEP in dollars FC CM%

CVP with fi xed profi t in units FC � P CM

CVP with fi xed profi t in dollars FC � P CM%

CVP with specifi ed profi t in units FC CM � Pu

CVP with profi t specifi ed as percentage of sales FC CM% � Pu%

where FC � fi xed cost CM � contribution margin per unit

CM% � contribution margin percentage P � total profi t (on a before-tax basis) Pu � profi t per unit (on a before-tax basis)

Pu% � profi t percentage per unit (on a before-tax basis)

To convert after-tax profi t to before-tax profi t, divide after-tax profi t by (1 � tax rate).

Margin of Safety (MS), p. 399Margin of Safety in Units � Actual Sales in Units � Break-Even Sales in Units

Margin of Safety in Dollars � Actual Sales $ � Break-Even Sales $

Margin of Safety % � (Margin of Safety in Units or $) � (Actual Sales in Units or $)

Degree of Operating Leverage (DOL), p. 400Degree of Operating Leverage � Contribution Margin � Profit before Tax

Predicted Profit � [1 � (DOL × Percent Change in Sales)] × Current Profit

Demonstration Problem

Green Th umb makes small plant stands that sell for $25 each. Th e company’s annual level of production and sales is 120,000 units. In addition to $430,500 of fi xed manufacturing overhead and $159,050 of fi xed administrative expenses, the following per-unit costs have been determined for each plant stand:

Direct material $ 6.00

Direct labor 3.00

Variable manufacturing overhead 0.80

Variable selling expense 2.20

Total variable cost $12.00

Required:a. Prepare a variable costing income statement at the current level of production and

sales.


b. Calculate the unit contribution margin in dollars and the contribution margin ratio for a plant stand.

c. Determine the break-even point in number of plant stands.

d. Calculate the dollar break-even point using the contribution margin ratio.

e. Determine Green Th umb’s margin of safety in units, in sales dollars, and as a percentage.

f. Compute the company’s degree of operating leverage. If sales increase by 25 percent, by what percentage will before-tax income increase?

g. How many plant stands must the company sell to earn $996,450 in before-tax income?

h. If the company wants to earn $657,800 after tax and is subject to a 20 percent tax rate, how many units must be sold?

i. How many plant stands must be sold to break even if Green Th umb’s fi xed manufacturing cost increases by $7,865? (Use the original data.)

j. Th e company has received an off er from a Brazilian company to buy 4,000 plant stands at $20 per unit. Th e per-unit variable selling cost of the additional units will be $2.80 (rather than $2.20), and $18,000 of additional fi xed administrative cost will be incurred. Th is sale would not aff ect domestic sales or their cost. Based on quantitative factors alone, should Green Th umb accept this off er?

Solution to Demonstration Problema. Green Thumb

Variable Costing Income Statement

Sales (120,000 × $25.00) $3,000,000

Variable production cost

Direct material (120,000 × $6.00) $720,000

Direct labor (120,000 × $3.00) 360,000

Overhead (120,000 × $0.80) 96,000

Variable selling expenses (120,000 × $2.20) 264,000 (1,440,000)

Contribution margin $1,560,000

Fixed cost

Manufacturing overhead $430,500

Administrative 159,050 (589,550)

Income before income tax $ 970,450

b. CM � SP � VC � $25 � $12 � $13 per unit

CM% � CM � SP � $13 � $25 � 52 percent

c. BEP � FC � CM � $589,550 � $13 � 45,350 plant stands

d. BEP � FC � CM% � $589,550 � 0.52 � $1,133,750 in sales

e. MSu � Current unit sales � BEP unit sales � 120,000 � 45,350 � 74,650 plant

stands

MS$ � Current sales in dollars � BEP sales in dollars � $3,000,000 � $1,133,750 � $1,866,250

MS% � MS in units � Current unit sales � 74,650 � 120,000 � 62 percent (rounded)

f. DOL � Current CM � Current Pre-Tax Income � $1,560,000 � $970,450 � 1.61 (rounded)


Increase in Income � DOL � % Increase in Sales � 1.61 � 0.25 � 40.25 percent

Proof:

New Sales � 120,000 � 1.25 � 150,000

New CM � 150,000 � $13.00 � $1,950,000

New Pre-Tax Profi t � New CM � FC � $1,950,000 � $589,550 � $1,360,450

Increase � New Pre-Tax Profi t � Old Pre-Tax Profi t � $1,360,450 � $970,450 � $390,000

Increase in % terms � $390,000 � $970,450 � 40.19 percent (rounded)

g. $13X � $589,550 � $996,450

X � $1,586,000 � $13

X � 122,000 plant stands

h. PBT � PAT � (1 � tax rate) � $657,800 � (1 � 0.20) � $657,800 � 0.80 � $822,250

$13X � $589,550 � $822,250

X � $1,411,800 � $13

X � 108,600 plant stands

i. X � Increase in FC � CM

X � $7,865 � $13

X � 605 units over BEP

New BEP � 45,350 � 605 � 45,955 plant stands

j. New CM for each additional unit � $20.00 � $12.60 � $7.40

Total New CM � $7.40 � 4,000 � $29,600

Increase in Pre-Tax Profi t � Increase in CM � Increase in FC � $29,600 � $18,000 � $11,600

Yes, the company should accept the off er.

Potential Ethical Issues

1. Ignoring the relevant range when setting assumptions about cost behavior to disregard the implications of cost changes on the calculation of BEP or CVP analysis

2. Treating some or all fi xed costs as per-unit costs (i.e., using absorption costing) in calculating BEP or performing CVP analysis

3. Using untested or inaccurate assumptions about the relationship between variables such as advertising and sales volume or sales price and sales volume to assure a particular decision outcome

4. Assuming a constant sales mix ratio while ignoring expected changes in demand for individual products when conducting CVP analysis for multiproduct fi rms

5. Using CVP analyses to support long-term cost management strategies

6. Visually distorting BEP graphs to project improper conclusions

7. Including irrelevant information in incremental analysis to manipulate calculation results

Ethics


Questions

1. What information provided by a variable costing income statement is used in computing the break-even point? Is this information on an absorption costing income statement? Explain your answer.

2. How is “break-even point” defi ned? What are the diff erences among the formula, graph, and income statement approaches for computing breakeven?

3. What is the contribution margin ratio? How is it used to calculate the break-even point?

4. Why is CVP analysis generally used as a short-run tool? Would CVP ever be appropriate as a long-run model?

5. How is the “bag” assumption used in CVP analysis for a multiproduct fi rm? What additional assumption must be made in multiproduct CVP analysis that doesn’t pertain to a single-product CVP situation?

6. A multiproduct company has a sales mix of nine widgees to three squigees. Widgees have a contribution margin ratio of 45 percent, and squigees have a contribution margin ratio of 80 percent. If the sales mix changes to six widgees to six squigees, will the company have a higher or lower weighted average contribution margin ratio and a higher or lower break-even point (in sales dollars)? Explain the rationale for your answer.

7. Defi ne and explain the relationship between margin of safety and degree of operating leverage.

Exercises

8. LO.1 (Variable costing income statement) Tasty Beverages began business in 2010 selling bottles of a thirst-quenching drink. Production for the fi rst year was 104,000 bottles, and sales were 98,000 bottles. Th e selling price per bottle was $3.10. Costs incurred during the year were as follows:

Ingredients used $ 56,000

Direct labor 26,000

Variable overhead 48,000

Fixed overhead 5,200

Variable selling expenses 10,000

Fixed selling and administrative expenses 28,000

Total actual cost $173,200

For 2010:

a. What was the production cost per bottle under variable costing?

b. What was variable cost of goods sold?

c. What was the contribution margin per bottle?

d. What was the contribution margin ratio?

9. LO.1 (Variable costing income statement) High Flight Toys manufactures frisbees. Th e following information is available for 2010, the company’s fi rst year in business when it produced 300,000 units. Revenue of $480,000 was generated by the sale of 180,000 frisbees.


Variable Cost Fixed Cost

Production

Direct material $150,000

Direct labor 100,000

Overhead 75,000 $112,500

Selling and administrative 90,000 100,000

a. What is the variable production cost per unit?

b. What is the total contribution margin per unit?

c. Prepare a variable costing income statement.

10. LO.2 (Cost and revenue behavior) Th e following fi nancial data have been deter-mined from analyzing the records of Tim’s Brake Co. (a one-product fi rm):

Contribution margin per unit $ 50

Variable cost per unit 42

Annual fi xed cost $180,000

How does each of the following measures change when product volume goes up by one unit at Tim’s Brake Co?

a. Total revenue

b. Total cost

c. Income before tax

11. LO.2 (Break-even point) Monet’s Prints has the following revenue and cost functions:

Revenue � $60 per unit

Cost � $120,000 � $30 per unit

a. What is the break-even point in units?

b. What is the break-even point in dollars?

12. LO.2 (Break-even point) Diamond Jim’s makes and sells class rings for local schools. Operating information is as follows:

Selling price per ring $600

Variable cost per ring

Rings and stones $220

Sales commissions 48

Overhead 32

Annual fi xed cost

Selling expenses $180,000

Administrative expenses 105,000

Manufacturing 60,000

a. What is Diamond Jim’s break-even point in rings?

b. What is Diamond Jim’s break-even point in sales dollars?

c. What would Diamond Jim’s break-even point be if sales commissions increased to $54?

d. What would Diamond Jim’s break-even point be if selling expenses decreased by $6,000?

Excel


13. LO.2 (Formula; graph; income statement) Pittsburg Tar Co. had the following income statement for 2010:

Sales (30,000 gallons × $8) $240,000

Variable cost

Production (40,000 gallons × $3) $120,000

Selling (30,000 gallons × $0.50) 15,000 (135,000)

Contribution margin $105,000

Fixed cost

Production $ 46,000

Selling and administrative 6,200 (52,200)

Income before tax $ 52,800

Income tax (40%) (21,120)

Net income $ 31,680

a. Compute the break-even point using the equation approach.

b. Prepare a CVP graph to refl ect the relationships among cost, revenue, profi t, and volume.

c. Prepare a profi t-volume graph.

d. Prepare a short explanation for company management about each of the graphs.

e. Prepare an income statement at break-even point using variable costing.

14. LO.3 (CVP) Seattle Leisure Designs has designed a new athletic suit. Th e company plans to produce and sell 30,000 units of the new product in the coming year. Annual fi xed costs are $600,000, and variable costs are 70 percent of selling price. If the company wants a pre-tax profi t of $300,000, at what minimum price must it sell its product?

15. LO.3 (CVP) Sheridan Shacks makes portable garden sheds that sell for $1,800 each. Costs are as follows:

Per Unit Total

Direct material $800

Direct labor 90

Variable production overhead 60

Variable selling and administrative cost 50

Fixed production overhead $200,000

Fixed selling and administrative 60,000

a. How many garden sheds must the company sell to break even?

b. If Sheridan Shacks’ management wants to earn a pre-tax profi t of $200,000, how many garden sheds must it sell?

c. If Sheridan Shacks’ management wants to earn a pre-tax profi t of $280,000, how many garden sheds must it sell?

16. LO.3 (CVP) Bill’s Cabinets sells a product for $360 per unit. Th e company’s variable cost per unit is $60 for direct material, $50 per unit for direct labor, and $34 per unit for overhead. Annual fi xed production overhead is $74,800, and fi xed selling and admin-istrative overhead is $50,480.

a. What is the contribution margin per unit?

b. What is the contribution margin ratio?

Excel


c. What is the break-even point in units?

d. Using the contribution margin ratio, what is the break-even point in sales dollars?

e. If Bill’s Cabinets wants to earn a pre-tax profi t of $51,840, how many units must the company sell?

17. LO.3 (CVP; taxes) Use the information for Sheridan Shacks in Exercise 15 and assume a tax rate for the company of 35 percent.

a. If Sheridan Shacks wants to earn an after-tax profi t of $182,000, how many garden sheds must it sell?

b. How much revenue is needed to yield an after-tax profi t of 8 percent of revenue? How many garden sheds does this revenue amount represent?

18. LO.3 (CVP; taxes) Use the information for Bill’s Cabinets in Exercise 16 and assume a tax rate for the company of 30 percent.

a. If Bill’s Cabinets wants to earn an after-tax profi t of $135,800, how many units must the company sell?

b. If Bill’s Cabinets wants to earn an after-tax profi t of $5.60 on each unit sold, how many units must the company sell?

19. LO.3 (Incremental sales) Dallas Offi ce Systems has annual sales of $2,250,000 with variable expenses of 60 percent of sales and fi xed expenses per month of $25,000. By how much must annual sales increase for Dallas Offi ce Systems to have pre-tax income equal to 30 percent of sales?

20. LO.3 (CVP; taxes) Golf Glider makes gasoline-powered golf carts. Th e selling price is $5,000 each, and costs are as follows:

Cost Per Unit Total

Direct material $2,000

Direct labor 625

Variable overhead 325

Variable selling 50

Annual fi xed production overhead $250,000

Annual fi xed selling and administrative 120,000

Golf Glider’s income is taxed at a 40 percent rate.

a. How many golf carts must Golf Glider sell to earn $600,000 after tax?

b. What level of revenue is needed to yield an after-tax income equal to 20 percent of sales?

21. LO.3 (Writing; Internet) A signifi cant trend in business today is the increasing use of outsourcing. Go to the Internet and search Web sites with the objective of gaining an understanding of the vast array of outsourcing services that are available. Prepare a presentation in which you discuss the extensive use of outsourcing today and how it could be used as a tool to manage a fi rm’s cost structure and in CVP planning.

22. LO.3 (Volume and pricing) Dim Witt is the county commissioner of Clueless County. He decided to institute tolls for local ferry boat passengers. After the tolls had been in eff ect for four months, Astra Astute, county accountant, noticed that collecting $1,450 in tolls incurred a daily cost of $2,000. Th e toll is $0.50 per passenger.

a. How many people are using the ferry boats each day?

b. If the $2,000 cost is entirely fi xed, how much must each passenger be charged for the toll process to break even? How much must each passenger be charged for the toll process to make a profi t of $250 per day?

Internet

Excel


c. Assume that only 80 percent of the $2,000 is fi xed and the remainder varies by pas-senger. If the toll is raised to $0.60 per person, passenger volume is expected to fall by 10 percent. If the toll is raised and volume falls, will the county be better or worse off than it is currently and by what amount?

d. Assume that only 80 percent of the $2,000 is fi xed and the remainder varies by pas-senger. If passenger volume will decline by 5 percent for every $0.20 increase from the current $0.50 rate, at what level of use and toll amount would the county fi rst make a profi t?

e. Discuss the saying “We may be showing a loss, but we can make it up in volume.”

23. LO.3 (CVP analysis) Following are abbreviated income statements for two companies, Ainsley and Bard:

Ainsley Bard

Sales $2,000,000 $2,000,000

Variable cost (1,400,000) 0

Contribution margin $ 600,000 $2,000,000

Fixed cost 0 (1,400,000)

Operating income $ 600,000 $ 600,000

Ainsley and Bard produce an identical product and both sell that product at $40. Both companies are searching for ways to increase operating income. Managers of both companies are considering three identical strategies. Consider each of the following strategies, and discuss which company is best situated to adopt that strategy.

a. Decrease sales price 30 percent to increase sales volume 60 percent.

b. Increase sales price per unit 30 percent, which will cause sales volume to decline by 15 percent.

c. Increase advertising by $200,000 to increase sales volume by 15,000 units.

24. LO.4 (CVP; multiproduct) Mel’s Male Accessories sells wallets and money clips. Historically, the fi rm’s sales have averaged three wallets for every money clip. Each wallet has an $8 contribution margin, and each money clip has a $6 contribution mar-gin. Mel’s incurs fi xed cost in the amount of $180,000. Th e selling prices of wallets and money clips, respectively, are $30 and $15. Th e corporate-wide tax rate is 40 percent.

a. How much revenue is needed to break even? How many wallets and money clips does this represent?

b. How much revenue is needed to earn a pre-tax profi t of $150,000?

c. How much revenue is needed to earn an after-tax profi t of $150,000?

d. If Mel’s earns the revenue determined in (b) but does so by selling fi ve wallets for every two money clips, what would be the pre-tax profi t (or loss)? Why is this amount not $150,000?

25. LO.4 (Multiproduct) Mean Machine makes three types of electric scooters. Th e com-pany’s total fi xed cost is $1,080,000,000. Selling prices, variable cost, and sales percent-ages for each type of scooter follow:

Selling Price Variable CostPercent of

Total Unit Sales

Mod $2,200 $1,900 30

Rad 3,700 3,000 50

X-treme 6,000 5,000 20


a. What is Mean Machine’s break-even point in units and sales dollars?

b. If the company has an after-tax income goal of $1 billion and the tax rate is 50 per-cent, how many units of each type of scooter must be sold for the goal to be reached at the current sales mix?

c. Assume the sales mix shifts to 50 percent Mod, 40 percent Rad, and 10 percent X-treme. How does this change aff ect your answer to part (a)?

d. If Mean Machine sold more X-treme scooters and fewer Mod scooters, how would your answers to parts (a) and (b) change? No calculations are needed.

26. LO.5 (CVP; margin of safety) Sid Simon wants to cash in on the increased demand for ethanol. Accordingly he purchased a corn farm in Iowa. Simon believes his corn crop can be sold to an ethanol plant for $4.80 per bushel. Variable cost associated with growing and selling a bushel of corn is $3.80. Simon’s annual fi xed cost is $132,000.

a. What is the break-even point in sales dollars and bushels of corn? If Simon’s farm is 1,200 acres, how many bushels must he produce per acre to break even?

b. If Simon actually produces 174,000 bushels, what is the margin of safety in bushels, in dollars, and as a percentage?

27. LO.5 (CVP; operating leverage; income statement) Racine Tire Co. manufactures tires for all-terrain vehicles. Th e tires sell for $60 and variable cost per tire is $30; monthly fi xed cost is $450,000.

a. What is the break-even point in units and sales dollars?

b. If Ronnie Rice, the company’s CEO, wants the business to earn a pre-tax profi t of 25 percent of revenues, how many tires must be sold each month?

c. If the company is currently selling 20,000 tires monthly, what is the degree of oper-ating leverage?

d. If the company can increase sales volume by 15 percent above the current level, what will be the increase in net income? What will be the new net income? Prove your calculations with an income statement.

28. LO.5 (Operating leverage; margin of safety; income statement) Tennessee Tonic makes a high-energy protein drink. Th e selling price per gallon is $7.20, and variable cost of production is $4.32. Total fi xed cost per year is $316,600. Th e company is currently selling 125,000 gallons per year.

a. What is the margin of safety in gallons?

b. What is the degree of operating leverage?

c. If the company can increase sales in gallons by 30 percent, what percentage increase will it experience in income? Prove your answer using the income statement approach.

d. If the company increases advertising by $41,200, sales in gallons will increase by 15 percent. What will be the new break-even point? Th e new degree of operating leverage?

29. LO.5 (Leverage factors; writing) A group of prospective investors has asked for your help in understanding the comparative advantages and disadvantages of start-ing a company that is either labor intensive or, in contrast, one that uses signifi cant cutting-edge technology and is therefore capital intensive. Prepare a report addressing the issues. Include discussions regarding cost structure, BEP, CVP, MS, DOL, risk, customer satisfaction, and the relationships among these concepts.

30. LO.6 (Product cost; writing) A friend of yours, attending another university, states she learned that CVP is a short-run-oriented model and is, therefore, of limited useful-ness. Your professor, however, has often discussed CVP in presentations about long-run


planning to your cost accounting class. You decide to investigate your friend’s allegation by preparing a report addressing your friend’s contention. Your professor is also ask-ing you to prepare a separate report for internal management’s use that addresses how the CVP model could be adapted to become more useful for making long-run deci-sions. Prepare these two reports, one for your friend’s understanding and one for your professor.

31. LO.2–LO.4 (Comprehensive) Compute the answers to each of the following inde-pendent situations.

a. Orlando Ray sells liquid and spray mouthwash in a sales mix of 1:2, respectively. Th e liquid mouthwash has a contribution margin of $10 per unit; the spray’s CM is $5 per unit. Annual fi xed cost for the company is $100,000. How many units of spray mouthwash would Orlando Ray sell at the break-even point?

b. Piniella Company has a break-even point of 4,000 units. At BEP, variable cost is $6,400 and fi xed cost is $1,600. If one unit over breakeven is sold, what will be the company’s pre-tax income?

c. Montreal Company’s product sells for $10 per bottle. Annual fi xed costs are $216,000 and variable cost is 40 percent of selling price. How many units would Montreal Company need to sell to earn a 25 percent pre-tax profi t on sales?

d. York Mets Company has a BEP of 2,800 units. Th e company currently sells 3,200 units at $65 each. What is the company’s margin of safety in units, in sales dollars, and as a percentage?

32. LO.6 (Ethics; writing) Niobrara Pesticide Company’s new president has learned that, for the past four years, the company has been dumping its industrial waste into the local river and falsifying reports to authorities about the levels of suspected car-cinogens in that waste. Th e plant manager says that there is no proof that the waste causes cancer and that only a few fi shing villages are within 100 miles downriver. If the company must treat the substance to neutralize its potentially injurious eff ects and then transport it to a legal dump site, the company’s variable and fi xed costs would rise to a level that might make the fi rm uncompetitive. If the company loses its competitive advantage, 10,000 local employees could become unemployed and the town’s economy could collapse.

a. What specifi c variable and fi xed costs can you identify that would increase (or decrease) if the waste were treated rather than dumped? How would these costs aff ect product contribution margin?

b. What ethical confl icts does the president face?

c. What rationalizations can you detect that plant employees have devised?

d. What options and suggestions can you off er the president?

33. LO.6 (CVP assumptions) Identify which of the CVP assumptions is violated in each of the circumstances described below.

a. Price per unit declines as the volume of sales and production increase.

b. Labor productivity increases as the volume of production declines.

c. Th e sales mix in a multiproduct fi rm varies as the volume of total sales changes.

d. Mixed cost cannot be separated into variable and fi xed components.

e. Costs behave according to a curvilinear function.

f. Sales and production volume diff er.

g. Fixed cost and capacity can be adjusted within the period.

34. LO.6 (CVP assumptions; writing) A local businesswoman, Jane Aire, has hired you and a colleague, Joanna, from your cost accounting class to advise her regarding her

Ethics


small manufacturing business that makes leather valises. Th e business was organized just two years ago and has failed to become profi table, which is why the business owner has hired you and Joanna. After analyzing the client’s books, Joanna prepared the fol-lowing simple income statement for the current year.

Sales $200,000

Variable cost (120,000)

Contribution margin $ 80,000

Fixed cost (140,000)

Operating loss $ (60,000)

After studying the income statement, Joanna worked out the break-even point for the fi rm and advised the client, “Ms. Aire, you will need to achieve sales of $350,000 before this business is producing enough revenues to cover all cost.”

Ms. Aire replied, “Th at’s a 75 percent increase over existing sales; I don’t see any way this business will reach that level of sales.”

“Th en,” said Joanna, “you should shut the business down today to cut your losses.”

After considering Joanna’s income statement and the conversation between Joanna and Aire, discuss whether you agree with Joanna’s recommendation.

Problems

35. LO.1 & LO.2 (Variable costing; ethics) In its fi rst year of operations, Utah Utility Trailers incurred the following costs:

Variable production cost $ 2,800 per unit

Variable selling and administrative cost 200 per unit

Fixed production cost $200,000

Fixed selling and administrative cost 80,000

For the year, the company reported the following results:

Sales ($5,000 per unit) $500,000

Cost of Goods Sold (400,000)

Gross Margin $100,000

Selling and Administrative Cost (100,000)

Operating Income $ 0

a. Using the contribution margin ratio approach, compute the break-even point for this company.

b. How many units did the fi rm produce in its fi rst year of operations?

c. Provide an explanation that reconciles your result in (a) to the income statement provided above.

d. Prepare a variable costing income statement for sales of 100 units.

e. Assume that Utah Utility Trailers is in need of a bank loan. Would it be unethical to use the income statement above, rather than the income statement compiled in (d), to present to the loan offi cer? Explain.

Ethics


36. LO.1–LO.3 (CVP) Casper Karts manufactures a three-wheeled shopping cart that sells for $60. Variable manufacturing and variable selling cost are, respectively, $35 and $10 per unit. Annual fi xed cost is $975,000.

a. What is the contribution margin per unit and the contribution margin ratio?

b. What is the break-even point in units?

c. How many units must the company sell to earn a pre-tax income of $900,000?

d. If the company’s tax rate is 40 percent, how many units must be sold to earn an after-tax profi t of $750,000?

e. If labor costs are 60 percent of the variable manufacturing cost and 40 percent of the fi xed cost, how would a 10 percent decrease in both variable and fi xed labor costs aff ect the break-even point?

f. Assume that the total market for three-wheeled shopping carts is 600,000 units per year and that Casper Karts currently has 18 percent of the market. Th e company wants to obtain a 25 percent market share and also wants to earn a pre-tax profi t of $1,350,000. By how much must variable cost be reduced? Provide some suggestions for variable cost reductions.

37. LO.1–LO.3 & LO.5 (CVP single product; comprehensive) Beantown Baseball Company makes baseballs that sell for $13.00 per two-pack. Current annual production and sales are 960,000 baseballs. Costs for each baseball are as follows:

Direct material $2.00

Direct labor 1.25

Variable overhead 0.50

Variable selling expenses 0.25

Total variable cost $4.00

Total fi xed overhead $1,250,000

a. Calculate the unit contribution margin in dollars and the contribution margin ratio for the company.

b. Determine the break-even point in number of baseballs.

c. Calculate the dollar break-even point using the contribution margin ratio.

d. Determine the company’s margin of safety in number of baseballs, in sales dollars, and as a percentage.

e. Compute the company’s degree of operating leverage. If sales increase by 30 percent, by what percentage would pre-tax income increase?

f. How many baseballs must the company sell if it desires to earn $1,096,000 in pre-tax profi t?

g. If the company wants to earn $750,000 after tax and is subject to a 40 percent tax rate, how many baseballs must be sold?

h. How many baseballs would the company need to sell to break even if its fi xed cost increased by $50,000? (Use original data.)

i. Beantown Baseball Company has received an off er to provide a one-time sale of 20,000 baseballs at $8.80 per two-pack to the Lowell Spinners. Th is sale would not aff ect other sales, nor would the cost of those sales change. However, the vari-able cost of the additional units would increase by $0.20 for shipping, and fi xed cost would increase by $6,000. Based solely on fi nancial information, should the company accept this off er? Show your calculations. What other factors should the company consider in accepting or rejecting this off er?


38. LO.1–LO.3 (CVP) Aqua Gear, in business since 2008, makes swimwear for profes-sional athletes. Analysis of the fi rm’s fi nancial records for the current year reveals the following:

Average swimsuit selling price $70

Variable swimsuit expenses

Direct material 28

Direct labor 12

Variable overhead 8

Annual fi xed cost

Selling $10,000

Administrative 24,000

Th e company’s tax rate is 40 percent. Samantha Waters, company president, has asked you to help her answer the following questions.

a. What is the break-even point in number of swimsuits and in dollars?

b. How much revenue must be generated to produce $40,000 of pre-tax earnings? How many swimsuits would this level of revenue represent?

c. How much revenue must be generated to produce $40,000 of after-tax earnings? How many swimsuits would this represent?

d. What amount of revenue would be necessary to yield an after-tax profi t equal to 20 percent of revenue?

e. Aqua Gear is considering purchasing a faster sewing machine that will save $6 per swimsuit in cost but will raise annual fi xed cost by $40,000. If the equipment is pur-chased, the company expects to make and sell an additional 5,000 swimsuits. Should the company make this investment?

f. A marketing consultant told Aqua Gear managers that they could increase the num-ber of swimsuits sold by 30 percent if the selling price was reduced by 10 percent and the company spent $10,000 on advertising. Th e company has been selling 3,000 swimsuits. Should the company make the changes advised by the consultant?

39. LO.1, LO.3, & LO.4 (CVP decision alternatives) Mons Weatherby owns a sports bro-kerage agency and sells tickets to major league baseball, football, and basketball games. He also sells sports travel packages that include game tickets, airline tickets, and hotel accommodations. Revenues are commissions based as follows:

Game ticket sales 8% commission

Airline ticket sales 10% commission

Hotel bookings sales 20% commission

Monthly fi xed costs include advertising ($2,200), rent ($1,800), utilities ($500), and other costs ($4,400). Th ere are no variable costs. A typical month generates the follow-ing sales amounts that are subject to the stated commission structure:

Game tickets $60,000

Airline tickets 9,000

Hotel bookings 14,000

Total $83,000

a. What is Weatherby’s normal monthly profi t or loss?

b. Weatherby estimates that airline bookings can be increased by 40 percent if he increases advertising by $1,200. Should he increase advertising?


c. Weatherby’s friend Rusty has asked him for a job in the travel agency. Rusty has proposed that he be paid 50 percent of whatever additional commissions he can bring to the agency plus a salary of $400 per month. Weatherby has estimated that Rusty can generate the following additional bookings per month:

Game tickets $ 8,000

Airline tickets 1,500

Hotel bookings 6,000

Total $15,500

Hiring Rusty would also increase fi xed cost by $600 per month inclusive of salary. Should Weatherby hire Rusty?

d. Weatherby hired Rusty and in the fi rst month, Rusty generated an additional $13,000 of bookings for the agency. Th e bookings, however, were all airline tickets. Was the decision to hire Rusty a good one? Why or why not?

40. LO.2 (Graph) Th e Real Deal is a social organization that performs charitable work in its local community. Th e club has the following monthly cost and fee informa-tion: monthly membership fee per member, $60; monthly variable cost of service per member, $25; and monthly fi xed service cost, $3,500. Costs are extremely low because volunteers provide almost all services and supplies. Excess of fees over service cost are used to support charitable activities.

a. Prepare a break-even chart for Th e Real Deal.

b. Prepare a profi t-volume graph for Th e Real Deal.

c. At this time, Th e Real Deal has only 120 members. Which of the preceding items (break-even chart or profi t-volume graph) would you use in a speech to the mem-bership about the benefi ts of recruiting additional members? Why?

41. LO.3 & LO.4 (Multiproduct fi rm) Yard Bird manufactures commercial and residential riding lawnmowers. Th e company sells one commercial mower per three residential mowers sold. Selling prices for the commercial and residential mowers are, respectively, $5,600 and $1,800, and variable selling and production cost are, respectively, $3,800 and $1,000. Th e company’s annual fi xed cost is $8,400,000. Compute the sales volume of each mower type needed to

a. break even.

b. earn $1,260,000 of income before tax.

c. earn $1,008,000 of income after tax, assuming a 40 percent tax rate.

d. earn 12 percent on sales revenue in pre-tax income.

e. earn 8 percent on sales revenue in after-tax income, assuming a 40 percent tax rate.

42. LO.3 & LO.4 (Multiproduct fi rm) Th e Glass Menagerie makes small pressed resin ducks and ducklings. For every duck sold, the company sells fi ve ducklings. Th e follow-ing information is available about the company’s selling prices and cost:

Ducks Ducklings

Selling price $24 $12

Variable cost 12 8

Annual fi xed cost $288,000

a. What is the average contribution margin ratio?

b. Calculate the monthly break-even point if fi xed cost is incurred evenly through-out the year. At the BEP, indicate how many units of each product will be sold monthly.


c. If the company wants to earn $96,000 pre-tax profi t monthly, how many units of each product must it sell?

d. Company management has specifi ed $31,680 as monthly net income, and the com-pany is in a 40 percent tax bracket. However, marketing information has indicated that the sales mix has changed to one duck to nine ducklings. How much total revenue and what number of products must be sold to achieve the company’s profi t objective?

e. Refer to the original information. If the company can reduce variable cost per duck-ling to $4 by raising monthly fi xed cost by $8,500, how will the break-even point change? Should the company make these changes? Explain your answer.

43. LO.3–LO.5 (Multiproduct fi rm) Th e Pink Flamingo, Inc., manufactures plastic lawn ornaments. Currently the fi rm manufactures three items: reindeer, snowmen, and fl a-mingos. For each reindeer, two snowmen and four fl amingos are sold.

Reindeer Snowmen Flamingos

Variable product cost $ 12.00 $15.00 $25.00

Variable selling expenses 6.00 4.50 8.00

Variable administrative expenses 3.00 5.50 6.00

Selling price 40.00 35.00 60.00

Annual fi xed factory overhead $420,000

Annual fi xed selling expenses 150,000

Annual fi xed administrative expenses 80,178

Th e fi rm is in a 40 percent tax bracket.

a. What is the annual break-even point in revenues?

b. How many reindeer, snowmen, and fl amingos are expected to be sold at the break-even point?

c. If the fi rm desires pre-tax income of $250,428, how much total revenue is required, and how many units of each product must be sold?

d. If the fi rm desires after-tax income of $155,718, how much total revenue is required, and how many units of each product must be sold?

e. If the fi rm achieves the revenue determined in (d), what is its margin of safety in dollars and as a percentage?

44. LO.2–LO.5 (Comprehensive; multiproduct) Nature’s Own makes three types of wood fl ooring: Oak, Hickory, and Cherry. Th e company’s tax rate is 40 percent. Th e following costs are expected for 2011:

Oak Hickory Cherry

Variable cost (on a per-square-yard basis)

Direct material $10.40 $6.50 $17.60

Direct labor 3.60 0.80 12.80

Production overhead 2.00 0.30 3.50

Selling expense 1.00 0.50 4.00

Administrative expense 0.40 0.20 0.60

Fixed overhead $760,000

Fixed selling expense 240,000

Fixed administrative expense 200,000


Per-square-yard expected selling prices are as follows: Oak, $32.80; Hickory, $16.00; and Cherry, $50.00. Th e expected sales mix is as follows:

Oak Hickory Cherry

Square yards 9,000 72,000 6,000

a. Calculate the break-even point for 2011.

b. How many square yards of each product are expected to be sold at the break-even point?

c. If the company wants to earn pre-tax profi t of $800,000, how many square yards of each type of fl ooring would it need to sell? How much total revenue would be required?

d. If the company wants to earn an after-tax profi t of $680,000, determine the revenue needed using the contribution margin percentage approach.

e. If the company achieves the revenue determined in part (d), what is the margin of safety (1) in dollars and (2) as a percentage?

45. LO2–LO.4 (CVP analysis; multiproduct) Ted Tyner owns Sixth Man Hotel, a luxury hotel with 60 two-bedroom suites for coaches and their players. Capacity is 10 coaches and 50 players. Each suite is equipped with extra-long king-sized beds, super-tall and extended shower heads, extra-tall bathroom vanities, a laptop, and a printer. Each suite has a Pacifi c Ocean view. Hotel services include airport limousine pickup and drop-off , a daily fruit basket, champagne on the day of arrival, and a Hummer for transportation. Coaches and players are interviewed about their dietary restrictions and room service requirements before arrival. Th e hotel’s original cost was $1,920,000, and depreciation is $160,000 per year. Other hotel operating costs include:

Labor $320,000 per year plus $5 per suite per day

Utilities $158,000 per year plus $1 per suite per day

Miscellaneous $100,000 per year plus $6 per suite per day

In addition to these costs, costs are also incurred on food and beverage for each guest. Th ese costs are strictly variable and (on average) are $40 per day for coaches and $15 per day for players.

a. Assuming that the hotel is able to maintain an average annual occupancy of 80 percent in both coach and player suites (based on a 360-day year), determine the minimum daily charge that must be assessed per suite per day to generate $240,000 of income before tax.

b. Assume that the per-day price Tyner charges is $240 for coaches and $200 for play-ers. If the sales mix is 12:48 (12 coach days of occupancy for every 48 player days of occupancy), compute the following:

1. Th e break-even point in total occupancy days.

2. Total occupancy days required to generate $400,000 of income before tax.

3. Total occupancy days to generate $400,000 of after-tax income. Tyner’s personal tax rate is 35 percent.

c. Tyner is considering adding a massage service for guests to complement current hotel services. He has estimated that the cost of providing such a service would largely be fi xed because all necessary facilities already exist. He would, however, need to hire fi ve certifi ed masseurs at a cost of $500,000 per year. If Tyner decides to add this service, how much would he need to increase his daily charges (assume equal dollar increases to coach and player room fees) to maintain the break-even point computed in (b)?


46. LO.3 (CVP analysis; advanced) Fairbanks Express is a luxury passenger carrier in Alaska. All seats are fi rst class, and the following data are available:

Number of seats per passenger train car 60

Average load factor (percentage of seats fi lled) 75%

Average full passenger fare $140

Average variable cost per passenger $60

Fixed operating cost per month $2,400,000

a. What is the break-even point in passengers and revenues per month?

b. What is the break-even point in number of passenger train cars per month?

c. If Fairbanks Express raises its average passenger fare to $170, it is estimated that the load factor will decrease to 60 percent. What will be the monthly break-even point in number of passenger cars?

d. (Refer to original data.) Fuel cost is a signifi cant variable cost to any railway. If crude oil increases by $16 per barrel, it is estimated that variable cost per passenger will rise to $80. What would be the new break-even point in passengers and in number of passenger train cars?

e. Fairbanks Express has experienced an increase in variable cost per passenger to $70 and an increase in total fi xed cost to $3,000,000. Th e company has decided to raise the average fare to $160. If the tax rate is 40 percent, how many passengers per month are needed to generate an after-tax profi t of $800,000?

f. (Use original data.) Fairbanks Express is considering off ering a discounted fare of $100, which the company believes would increase the load factor to 80 percent. Only the additional seats would be sold at the discounted fare. Additional monthly advertising cost would be $160,000. How much pre-tax income would the dis-counted fare provide Fairbanks Express if the company has 40 passenger train cars per day, 30 days per month?

g. Fairbanks Express has an opportunity to obtain a new route that would be traveled 15 times per month. Th e company believes it can sell seats at $150 on the route, but the load factor would be only 60 percent. Fixed cost would increase by $200,000 per month for additional crew, additional passenger train cars, maintenance, and so on. Variable cost per passenger would remain at $60.

1. Should the company obtain the route?

2. How many passenger train cars must Fairbanks Express operate to earn pre-tax income of $101,000 per month on this route?

3. If the load factor could be increased to 75 percent, how many passenger train cars must be operated to earn pre-tax income of $101,000 per month on this route?

4. What qualitative factors should be considered by Fairbanks Express in making its decision about acquiring this route?

47. LO.2, LO.3, & LO.5 (Incremental analysis) Calypso Canvas makes canvas window awnings. You have been asked to predict the potential eff ects of some proposed com-pany changes. Th e following information is available:

Variable cost per unit

Direct material $18.40

Direct labor 13.00

Production overhead 8.60

Selling expenses 4.60

Administrative expenses 3.00


Annual fi xed cost

Production overhead $1,200,000

Selling 960,000

Administrative 480,000

Th e selling price is $94.00 per unit, and expected sales volume for the current year is 150,000 units. Following are some changes proposed by various members of the company.

1. Engineers suggest that adding color accents to each unit at a cost of $14.40 would increase product sales by 20 percent.

2. Th e sales manager suggests that a $520,000 increase in advertising will increase sales by 15 percent.

3. Th e sales force believes that lowering the price by 5 percent will increase demand in units by 10 percent.

a. Compute the current break-even point in units and dollars.

b. Compute the current margin of safety in dollars, in units, and as a percentage.

c. Compute the independent effects on profit and dollar break-even point of each of the suggestions. For each proposal, advise company management about acceptability.

48. LO.1–LO.3 & LO.5 (MS; DOL; PV graph) You are considering buying one of two local fi rms (Olson Corp. and Miami Inc.). Olson Corp. uses a substantial amount of direct labor in its manufacturing operations and its salespeople work on com-mission. Miami Inc. uses the latest automated technology in manufacturing; its salespeople are salaried. Th e following fi nancial information is available for the two companies:

OLSON CORP. MIAMI INC.

2010 2011 2010 2011

Sales $600,000 $960,000 $600,000 $840,000

Expenses including taxes (528,000) (823,200) (528,000) (667,200)

Net income $ 72,000 $136,800 $ 72,000 $172,800

After examining cost data, you fi nd that the fi xed cost for Olson Corp. is $60,000; the fi xed cost for Miami Inc. is $300,000. Th e tax rate for both companies is 40 percent.

a. Recast the income statements into a variable costing format.

b. What are the break-even sales for each fi rm for each year?

c. Assume that you could acquire either fi rm for $1,200,000, and you want an after-tax return of 12 percent on your investment. Determine what sales level for each fi rm would allow you to reach your goal.

d. What is the margin of safety for each fi rm for each year? What is the degree of operating leverage?

e. Assume that product demand for 2012 is expected to rise by 15 percent from the 2011 level. What will be the expected net income for each fi rm?

f. Assume that product demand for 2012 is expected to fall by 20 percent from the 2011 level. What will be the expected net income for each fi rm?

g. Prepare a profi t-volume graph for each fi rm.

Excel


49. LO.5 (CVP; DOL; MS—two quarters; comprehensive) Following is information pertaining to Dayton Co.’s operations of the fi rst and second quarter of 2010:

QUARTER

First Second

Units

Production 70,000 60,000

Sales 60,000 70,000

Expected activity level 65,000 65,000

Unit selling price $ 75.00 $ 75.00

Unit variable costs

Direct material $ 34.50 $ 34.50

Direct labor 16.50 16.50

Factory overhead 7.80 7.80

Selling and administrative 5.70 5.70

Fixed costs

Factory overhead $195,000 $195,000

Selling and administrative 42,800 42,800

Additional Information

Th ere were no fi nished goods at January 1, 2010.•

Dayton Co. writes off any quarterly underapplied or overapplied overhead as an • adjustment to Cost of Goods Sold.

Dayton Co.’s income tax rate is 35 percent.•

a. Prepare a variable costing income statement for each quarter.

b. Calculate each of the following for 2010 if 260,000 units were produced and sold:

1. Unit contribution margin.

2. Contribution margin ratio.

3. Total contribution margin.

4. Net income.

5. Degree of operating leverage.

6. Annual break-even unit sales volume.

7. Annual break-even dollar sales volume.

8. Annual margin of safety as a percentage.

9. Annual margin of safety in units.

50. LO.6 (CVP assumptions; writing) You were talking to your roommate one day about CVP analysis and the approaches that are used to calculate the break-even point. You also described the assumptions that underlie this type of analysis.

Your roommate proclaimed, “Wow, you people in accounting are pretty simple. Do you realize how unrealistic it is to assume that, no matter how many units you sell, you will realize the same price per unit? And, I’ve never heard any serious person suggest that costs are linear. How can you possibly state that assumption with a straight face? In your world, profi t maximization is simple . . . just produce the maximum amount possible.”

Provide a written justifi cation of the assumptions accountants make in conducting CVP analysis that will satisfy your critical economist roommate.


51. LO. 2; LO.3; LO.5 ( CVP; DOL; decision making) Atlantic Fish Company is a whole-sale distributor of cod. Th e company services restaurants in the Boston area. Small but steady growth in sales has been achieved by Atlantic Fish Company over the past few years, while cod prices have been increasing. Th e company is formulating its plans for 2010 and has gathered the following information:

Average selling price per pound $9.00

Costs

Cost of cod per pound $5.60

Shipping expense per pound 0.40

Selling and administrative expense (rent and salaries) $650,000

Sales commissions 10% of sales

Expected annual sales volume for 2010: 400,000 pounds of cod

The company’s estimated tax rate is 40 percent.

a. What is the expected net income for the coming year? Prepare a contribution income statement.

b. Compute the contribution margin per unit and the contribution margin ratio.

c. What is the break-even point in pounds sold and revenues?

d. Compute the degree of operating leverage and margin of safety expected for the coming year.

e. Refer to the original data. Using the degree of operating leverage you computed in (d), compute the expected profi t if sales are 20% above the expected level.

f. Refer to the original data. How many pounds of cod must be sold to earn an after-tax net income of $900,000?

Documents

Chapter 9 Break-Even Point and Cost-Volume-Profit Analysis.pdf